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The product of the roots of a quadratic equation is 20 and the sum of its roots is (-8). What is the quadratic equation?
Consider the statements given below: A: Sum of roots of a quadratic equation ax2 + bx + c = 0 is (c/a). B: If one root of a quadratic equation is (p + qi), then root must be (q + pi). C: Roots of the equation 3x2 + 4x = 5 are all real. Which of the statement(s) is/are TRUE?
In quadratic equations aX2 + bX + c = 0 and dY2 + eY + f = 0, a, b and c are the coefficient of X2, X and constant term of aX2 + bX + c = 0 while d, e and f (are integers) and are the coefficient of Y2, Y and constant term of equation dY2 + eY + f = 0. If the ratio of sum of a and b together to the sum of b and c together is 11 : 6, a : b = 6 : 5, b2 = 4a + c, f2 = e + d – 3, d : e = 3 : 4, and e = 3f + 1 then find a quartic equation in Z(variable) whose roots are the roots of given equations.
A and B are positive roots of quadratic equation and (A + B)2 = 400 and (A – B)2 = 4. Find the quadratic equation whose roots are A and B.
If the roots of the quadratic equation x2 – x + 1 = 0 are α and β, then find the quadratic equation whose roots are α4 and β4.
The sum and the product of the roots of a quadratic equation are 7 and 12 respectively. If the bigger root is halved and the smaller root is doubled, then what is the resulting quadratic equation ?
Which of the following is true? A: If the sum of cube of three numbers is thrice the product of the three numbers, then the sum of three numbers will be non-zero. B: For quadratic equation ax2 + bx + c = 0, If b2 < 4ac, then the given equation has only one real root. C: In the equation, x2 – (a + b)x + ab = 0, the roots of this equation will be ‘a’, ‘b’.
Given two quadratic equations, I. x2 - 31x + 240 = 0 Equation I has two roots x1, x2. (x1 > x2) II. 3y2 – 7y – 3 = 8y - 3y2 - 9 Equation II has two roots y1, y2. (y2 > y1) Find the equation whose roots are (– 2y1 + x1), - (y2 – x2).
There is a quadratic equation 5x2 – 10x + p = 0, the product of roots of this equation is 4 times of sum of the roots, then what must be the value of p ?
Find the quadratic equation whose sum of roots is (-2) and the product of the roots is (-16)?